Method for Accurate and Efficient Eye Diagram Prediction of Nonlinear High-Speed Links

Signaling analysis of nonlinear high-speed circuits is challenging because it cannot rely on linear time-invariant principles, whereas an exhaustive nonlinear simulation is computationally prohibitive for low bit error rates. To find the worst-case eye, an exhaustive approach requires nonlinear simulations of $2^m$ bit patterns for a channel of $m$ -bit memory. In this article, we represent the nonlinear responses to the $2^m$ inputs by a rank- $k$ matrix, where $k$ denotes the number of distinct waveforms in the responses for a prescribed accuracy, which is much smaller than $2^m$ . We further develop a fast full cross approximation algorithm to find the rank- $k$ model with a low complexity independent of $2^m$ . Simulations of large-scale real-world nonlinear circuits with an over 100-bit channel memory demonstrate the accuracy, efficiency, and capacity of the proposed work.